The goal of this activity is for students to be reminded of the importance of measures of variability. Students reason abstractly and quantitatively (MP2) when they compare data sets and decide which is the better option. Students must explain their reasoning for choosing one of the options and use statistics to justify their answers. This activity helps students gain more practice working with using variability to compare data sets.

The purpose of this discussion is to compare how students made their decisions. Here are sample questions to promote class discussion:

• “How did the variability influence your choices?" (When there is greater variability, the values are more spread out, so that helped me think about whether I wanted consistent values or a wider range.)
• "What are some situations in which less variability might be preferred?" (When you want the results to be consistent and reliable. Examples include the number of points scored by a good player, the miles a car can go on a single gallon of gas, or the price of milk.)
• “How would the process of choosing the best situation be different if you were given a box plot?” (With a histogram or box plot, I wouldn’t have known exact numbers, so I would probably have to use a measure like IQR or the median to help make my decision.)

The purpose of this activity is to elicit the idea that extreme values tend to have little effect on the median and interquartile range, which will be useful when students explore the effects of outliers in a later activity.  The structure of Notice and Wonder gives space for students to notice and be curious about the extreme value in Tyler’s results. While students may notice and wonder many things about these data displays, the presence of extreme values and the stability of the median and quartiles are the important discussion points.

When students articulate what they notice and wonder, they have an opportunity to attend to precision in the language they use to describe what they see (MP6). They might first propose less formal or imprecise language, and then restate their observation with more precise language to communicate more clearly.

This prompt gives students opportunities to see and make use of structure (MP7). Students should use the structure of the data displays to notice that extreme values affect the mean and mean absolute deviation much more than median and interquartile range.

The purpose of this discussion is to make sure students understand that extreme values tend to have little effect on the median and interquartile range.   

Ask students to share the things they noticed and wondered. Record and display their responses without editing or commentary. If possible, record the relevant reasoning on or near the situation. Next, ask students, “Is there anything on this list that you are wondering about now?” Encourage students to observe what is on display and respectfully ask for clarification, point out contradicting information, or voice any disagreement.

If the effect of the extreme value on the measures of center and measures of variation does not come up during the conversation, ask students to discuss this idea.